static vs extern "C"/"C++"

Yes, you are just lucky :) The extern "C" is one language linkage for the C language that every C++ compiler has to support, beside extern "C++" which is the default. Compilers may supports other language linkages. GCC for example supports extern "Java" which allows interfacing with java code (though that's quite cumbersome).

extern "C" tells the compiler that your function is callable by C code. That can, but not must, include the appropriate calling convention and the appropriate C language name mangling (sometimes called "decoration") among other things depending on the implementation. If you have a static member function, the calling convention for it is the one of your C++ compiler. Often they are the same as for the C compiler of that platform - so i said you are just lucky. If you have a C API and you pass a function pointer, better always put one to a function declared with extern "C" like

extern "C" void foo() { ... }

Even though the function pointer type does not contain the linkage specification but rather looks like

void(*)(void)

The linkage is an integral part of the type - you just can't express it directly without a typedef:

extern "C" typedef void(*extern_c_funptr_t)();

The Comeau C++ compiler, in strict mode, will emit an error for example if you try to assign the address of the extern "C" function of above to a (void(*)()), beause this is a pointer to a function with C++ linkage.

Note, that extern C is the recommended way of C/C++ interoperability. Here is the master talking about it. To add to eduffy's answer: note that static functions and variables in the global namespace are deprecated. Use an anonymous namespace at least.

Back to extern C: if you don't use extern C you will have to know the exact mangled name and use it. That is much more of a pain.